Properties

Label 163170fx
Number of curves $1$
Conductor $163170$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("fx1")
 
E.isogeny_class()
 

Elliptic curves in class 163170fx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
163170.q1 163170fx1 \([1, -1, 0, 4695, 175825]\) \(10503459/18500\) \(-20156626696500\) \([]\) \(387072\) \(1.2377\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 163170fx1 has rank \(1\).

Complex multiplication

The elliptic curves in class 163170fx do not have complex multiplication.

Modular form 163170.2.a.fx

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - q^{11} + q^{16} + 5 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display